1. Evidence Based Medicine and Medical Decision Making Iztok Hozo, Professor of Mathematics Indiana University Northwest European School of Oncology How to Practice Evidence Based Oncology 22-24 July, 2004. Antwerp, Belgium (bug chunks taken from Ben. Djulbegovic – with permission)

2. Theories of decision-making normative theories what people “ought to do” axiomatic theories based on mathematical and statistical proofs, usually on expected utility theory the rationale or best course of action is the one that maximizes expected utility descriptive theories how people actually make decisions (“is” vs. “ought to”) people rarely make decisions in accord with normative theories (e.g. to avoid regret associated with wrong decisions) prescriptive theories since humans can be poor decision makers, prescriptive theory is concerned with the development of decision aids based on modification of normative theories, but also integrate other processes (such as attitudes, biases, values, etc)

3. Decision-Making how to deal with the uncertainty

4. Evidence and (normative) decision-making

5. Evidence Based Medicine The main focus of EBM has been understanding treatment effects (benefits and harms) usually expressed as one of the EBM therapeutic summary measures. These summary measures relate to the effects of the treatment on morbidity and mortality of a disease.

6. EBM therapeutic summary measures: Benefits relative risk reduction (efficacy, E, RRR) = the proportional reduction in rates of bad events (deaths) between experimental (Mrx) and control (no treatment) (M) group. = the proportional reduction in rates of bad events (deaths) between experimental (Mrx1) and control (Mrx2) treatment group.

7. EBM therapeutic summary measures: Benefits absolute risk reduction (risk difference, RD, ARD) = the actual difference in rates of bad events between experimental (Mrx, Mrx1) and control (no treatment, treatment2) (M, Mrx2) group. number needed to treat (NNT) = the reciprocal of the actual difference in rates of bad events between experimental (Mrx, Mrx1) and control (M, Mrx2) group. = the number of patients who need to be treated with the experimental treatment in order to prevent one bad outcome or attain one good outcome

8. EBM therapeutic summary measures: Treatment Harms Rates of adverse events due to treatment (R) number needed to harm (NNH) = the reciprocal of the actual difference in rates of bad adverse events between experimental (R, R1) and control (R2) group. = the number of patients who must be treated with the experimental treatment in order for one to experience a harmful event.

9. Decision Analysis is an explicit, quantitative method of clinical decision making that involves the separation of the probabilities of events from their relative values, or utilities. Utilities associated with a particular clinical outcome can be expressed in different units such as length of life, adjusted quality of life, morbidity or mortality rates, absence of pain, dollar value, or the strength of individual patient preference for an outcome.

10. Decision Analysis In choosing among several competing clinical scenarios, the optimal decision rests on selection of the strategy with the highest expected value, which is calculated by computing the average utilities of all possible results, weighted by their corresponding probabilities.

11. A Simple Decision Tree The first decision (blue square) is made by the physician. The second decision (green circle) is determined by the probability of the disease.

12. EBM + MDM If utilities can be expressed as the probability of freedom from the consequences of disease or the toxicity of treatment and if EBM therapeutic measures relate to the effects of the treatment on disease morbidity or mortality, then it is possible to integrate EBM indices within the framework of decision analysis.

13. A Simple Model (EBM utilities) Defining outcome utilities: U1 = U[D+,Rx] = (1-Mrx)*(1-R) = 1-Mrx-R+Mrx*R, or U1 =1-Mrx-R (Mrx*R 0 since the probability of Mrx & R occurring simultaneously in practice is usually nil; e.g. patient on chemoRx cannot die of breast cancer and toxic effects of chemoRx at the same time) U2 = U[D-,Rx1] = 1-R U3 = U[D+,NoRx] = 1-M U4 = U[D-,NoRx] = 1

14. Treatment No Treatment Disease No Disease 1 - M RX -R 1 - R 1 - M 1 p 1 - p p Treatment vs. No Treatment

15. Integration of EBM therapeutic measures within decision analysis Find the threshold probability, p t, at which we are indifferent between Rx vs NoRx:

16. The two expected values are equal when p*U1+(1-p)*U2 = p*U5+(1-p)*U6 Or in case of our utilities, p*(1-Mrx)*(1-R) +(1-p)*(1-R) = p*(1-M)+(1-p)*1 The solution of this equation is: Expected value of Treatment is E[Rx] = p*U1+(1-p)*U2 Expected value of not giving Treatment is E[NoRx] = p*U5+(1-p)*U6 Expected Values

17. The Threshold If the probability of a disease, pD, is greater than p t, then treatment should be given. If pD < p t, the treatment is not indicated.

18. A Clinical Example Kearon C, Gent M, Hirsh J, et al.: A comparison of three months of anticoagulation with extended anticoagulation for a first episode of idiopathic venous thromboembolism. N Engl J Med 1999; 340: 901-7 : a study in which they randomized patients who already completed a 3 month course of warfarin to determine if longer anticoagulation would be beneficial in the prevention of deep venous thrombosis (DVT) recurrence. the NNT for the prophylaxis of DVT recurrence is 4, i.e., 4 patients need to be treated with warfarin for 1 year in order to prevent one episode of DVT. however, the optimal duration of treatment needs to be interpreted in light of not only the benefit but also the harm of warfarin treatment.

19. While an NNT of 4 seems to represents a very effective therapy, this measure alone does not provide an answer to the question if this treatment is better than the alternative management strategy of observation without active treatment. To begin to address the clinical question whether to give warfarin or not, we note in the study by that the annual risk of major bleeding was 3.8% (compared to zero in placebo arm) representing an NNH=26. Based on the threshold analysis presented here, warfarin should be administered if the probability of DVT recurrence is greater than the threshold p = 15% (4/26). In this study, the recurrence rate for DVT was 27.4% per year suggesting that warfarin treatment should be continued beyond the initial 3 months of treatment in typical patients meeting eligibility criteria described in the Kearon study.

20. Treatment 1 Treatment 2 Disease No Disease 1 - M RX1 -R 1 1 - R 1 1 - M RX2 - R 2 1 - R 2 p 1 - p p Treatment 1 vs. Treatment 2

21. Find the threshold probability, p t, at which we are indifferent between administering treatment Rx1 or treatment Rx2. If the probability of a disease, pD, is greater than p t, then treatment should be given. If pD < p t, the treatment is not indicated. Threshold in case of two treatments

22. B) Minimal necessary efficacy at which therapy is worth considering (Rx1 vs Rx2): The following inequalities must be satisfied to even consider treatment Rx1 as opposed to alternative treatment Rx2: Or For example, as intuitively expected we should only give the treatment that provides better survival adjusted for risk difference between two treatment options.

23. When testing is an option: If the question is whether to administer treatment, perform test or continue observation, the solution of the model that includes testing as an option is provided by (the solution for riskless test only is provided): where LR+ is the positive likelihood ratio and is used in the case of the testing threshold (p=p tt ) and LR- is is the negative likelihood ratio of the test and is used in the case we want to determine test-treatment threshold (p=p rx ). Note that we should not even consider ordering the diagnostic test if treatment risk (R) is greater than its efficacy (E)(since p t <0).

25. Test threshold formulas If the probability of the disease (event) is less than p tt, continue with observation. If the probability is between the values of p tt and p rx, order the test. Finally, if the probability is larger than p rx, administer the treatment.

26. Conclusions EBM therapeutic summary measures are utilities and alone cannot be used in medical decision making Effective integration of EBM therapeutic summary measures of the treatment benefits and harms requires their linking to decision analysis When EBM therapeutic summary measures are linked to decision analysis, some new principles of clinical decision making emerge (such as never administer treatment or order a diagnostic test if treatment risk is greater than its efficacy)

27. Java Script Threshold Calculator HTTP://www.hsc.usf.edu/~bdjulbeg/ http://www.iun.edu/~mathiho/medmath/ medmath.htm